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The axioms are translated into a set of postulates about the substrate of consciousness (called a complex), which are then used to formulate a mathematical framework for assessing both the quality and quantity of experience. The explanatory identity proposed by IIT is that an experience is identical to the cause\u2013effect structure unfolded from a maximally irreducible substrate (a \u03a6-structure). In this work we introduce a definition for the integrated information of a system (\u03c6s) that is based on the existence, intrinsicality, information, and integration postulates of IIT. We explore how notions of determinism, degeneracy, and fault lines in the connectivity impact system-integrated information. We then demonstrate how the proposed measure identifies complexes as systems, the \u03c6s of which is greater than the \u03c6s of any overlapping candidate systems.<\/jats:p>","DOI":"10.3390\/e25020334","type":"journal-article","created":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T03:07:57Z","timestamp":1676257677000},"page":"334","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["System Integrated Information"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4779-6734","authenticated-orcid":false,"given":"William","family":"Marshall","sequence":"first","affiliation":[{"name":"Department of Psychiatry, University of Wisconsin-Madison, Madison, WI 53719, USA"},{"name":"Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2124-7147","authenticated-orcid":false,"given":"Matteo","family":"Grasso","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, University of Wisconsin-Madison, Madison, WI 53719, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9737-6260","authenticated-orcid":false,"given":"William G. 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